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2 years ago

13

Solve the missing variable. Show your process please because I did the other three on my homework sheet but I really struggle wi

th math. Will definitely give brainly because this means a lot :)
-8.4b - 4.2 = 12.6

Is this -2 or?

2 answers:

kotykmax [81]2 years ago

5 0

Follow these steps:

-8.4b - 4.2 = 12.6

Add 4.2 on both sides:

-8.4b = 16.8

Divide by -8.4 on both sides to give you the final answer of:

b = -2

So you're answer is indeed correct! Hope this helps and that the steps are clear enough!

tester [92]2 years ago

4 0

The big intention behind every step you take in these "find the value of x" problems is to isolate the x by doing PEMDAS in reverse and using the opposite operation. So I would do first is add the 4.2 on both sides. This is so that the 4.2 on the side of the x is canceled out. This makes
$- 8.4b = 16.8$
From here, since the opposite of multiplying is dividing, you divide both sides by -8.4. You can use a calculator to find the answer but you get
$b = - 2$

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2 years ago

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I know you want to answer this question.

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Step-by-step explanation:

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$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

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$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

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$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

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Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

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$u^{3}$

Substitute:

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Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

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